Simplify the expression. $(4a+7)(-3a+4)$
Solution: First distribute the ${4a+7}$ onto the ${-3a}$ and ${4}$ $ = {-3a}({4a+7}) + {4}({4a+7})$ Then distribute the ${-3a}.$ $ = ({-3a} \times {4a}) + ({-3a} \times {7}) + {4}({4a+7})$ $ = -12a^{2} - 21a + {4}({4a+7})$ Then distribute the ${4}$ $ = -12a^{2} - 21a + ({4} \times {4a}) + ({4} \times {7})$ $ = -12a^{2} - 21a + 16a + 28$ Finally, combine the $x$ terms. $ = -12a^{2} - 5a + 28$